Random Overlap Structures: Properties and Applications to Spin Glasses

Details Random Overlap Structures: Properties and Applications to Spin Glasses Random Overlap Structures: Properties and Applications to Spin Glasses

2010-11-08

arxiv.org/abs/1011.1823v2

Mathematics

Probability

34 pages, corrections in section 3 and Theorem 1.8

Scientific paper

Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits of Gibbs measures under the appropriate algebra of functions. We prove that the so called `cavity mapping' on the space of ROSt's is continuous, leading to a proof of the stochastic stability conjecture for the limiting Gibbs measures of a large class of spin glass models. Similar arguments yield the proofs of a number of other properties of ROSt's that may be useful in future attempts at proving the ultrametricity conjecture. Lastly, assuming that the ultrametricity conjecture holds, the setup yields a constructive proof of the Parisi formula for the free energy of the Sherrington-Kirkpatrick model by making rigorous a heuristic of Aizenman, Sims and Starr.

Affiliated with

Also associated with

No associations

Rating

Random Overlap Structures: Properties and Applications to Spin Glasses does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random Overlap Structures: Properties and Applications to Spin Glasses, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Overlap Structures: Properties and Applications to Spin Glasses will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131440